WO2006061491A1

WO2006061491A1 - Method for determining the value of a signal received and associated receiver

Info

Publication number: WO2006061491A1
Application number: PCT/FR2005/002998
Authority: WO
Inventors: Julien Poirrier; Michel Joindot; Benoît CHARBONNIER
Original assignee: France Telecom
Priority date: 2004-12-08
Filing date: 2005-12-01
Publication date: 2006-06-15

Abstract

The invention concerns a method for determining the value of a received signal, including the following steps: receiving a signal (x(t)) from a transmission channel; equalizing the received signal by summing several copies of the signal offset in time and weighted by respective coefficients (C0, C1, Cn); determining the value of the received signal from the equalized signal; determining an error signal (e) based on the difference between the equalized signal (y) and the determined value (d); and updating the coefficients based on the determined error signal. The invention is characterized in that the error signal comprises a weight of the difference between the equalized signal and the determined signal by at least one among a function (f1, f3) of the equalized signal and a function (f2, f4) of the determined value.

Description

METHOD FOR DECIDING THE VALUE OF A SIGNAL RECEIVED AND

ASSOCIATED RECEIVER

The present invention relates to the decision of the value of a received signal. Some transmission or communication channels are altered by time-varying distortions. This is the case, for example, with optical fibers and radio channels. In order to limit these alterations, it is known to perform an adaptive equalization of the signals received on such channels. This equalization consists, for example, in filtering the signals received using a transversal filter. Thus, the transverse linear equalizer ("Feedforward Equalizer" or FFE) and the recursive decision-equalizer (DFE) are classic examples for implementing equalization.

Equalization generally consists of summing several copies of a received signal, shifted in time and weighted by respective coefficients. The redundancy of information included in such a sum thus makes it possible to reduce intersymbol interference (ISI).

In addition, it is known to update the weighting coefficients using a least mean square ("Least Mean Square" or LMS) algorithm. The LMS algorithm aims to limit the bad decisions by minimizing the mean squared error based on the difference between the equalized signal and the value decided for the received signal considered. Such an algorithm offers very good performance when the transmission channels used have a Gaussian White Additive Noise (AWGN). It realizes indeed a good compromise between the increase of the noise resulting from the summation of the different copies of the received signal staggered in time and the reduction of I ¹ ISI.

Transmission channels are generally degraded by additive noise, typically thermal noise. There are, however, channels where the dominant noise is not additive but multiplicative.

Such channels are in particular the optical type channels, where the noise Spontaneous Emission ("ASE") is the main source of noise. Even if this noise ASE can be likened to an additive noise, the detection of the received signal, implementing an optoelectronic conversion, causes a beat ("beating") of the noise ASE with itself and with the signal. The ASE-ASE beat can be approximated by an additive noise. On the other hand, the ASE-signal beat constitutes a noise dependent on the signal, which can not be assimilated to an additive noise. In the optical case, the total noise is therefore not an additive noise, but a noise comprising an additive part and a multiplicative part (that is to say noise multiplied to the received signal). For the multiplicative part, the variance of the noise is proportional to the power of the received signal.

For such transmission channels having a noise dependent on the signal and therefore not comparable to an additive noise, the LMS algorithm is no longer optimal. This is also the case for channels with crosstalk ("coherent crosstalk"). In fact, the equalization adapted by the LMS does not make it possible to preserve the asymmetry of the noise on the transmission channels, in the presence of multiplicative noise in particular. The asymmetry of the noise is therefore reduced by the equalizer according to the LMS criterion, which leads to a degradation of the performance of the equalization. To overcome this problem, it has been proposed to replace the LMS with algorithms based on dithering. These algorithms use performance-related feedback parameters, such as an eye opening, a quality factor, a bit error rate estimate, and so on. However, these solutions proved to be very slow compared to the LMS. It has also been proposed to use algorithms of the LMS type but of order greater than 2. This solution has been described in the article "Adaptive Electronic Equalization Using Higher-Order Statistics for PMD Compensation in Long-Haul Fiber-Optic Systems". "Ut-Va Koc, Kun-Yii Tu ry Noriaki Kaneda (ECOC 2002). However, these algorithms make it possible to preserve the asymmetry of the noise only partially and they can not adapt according to the distribution between the additive noise and the multiplicative noise.

An object of the present invention is to overcome the disadvantages above.

A more particular object of the invention is to obtain better performances than with the LMS algorithm for the channels having a noise depending on the signal, seen from a receiver ensuring the detection of a signal transmitted on such channels.

The invention thus proposes a method for deciding the value of a received signal, comprising the following steps:

receive a signal from a transmission channel;

equalizing the received signal by summing several copies of the signal shifted in time and weighted by respective coefficients;

- decide the value of the received signal from the equalized signal;

determining an error signal dependent on a difference between the equalized signal and the decided value; and

updating said coefficients as a function of the determined error signal. According to the invention, the error signal comprises a weighting of the difference between the equalized signal and the value decided by at least one of a function of the equalized signal and a function of the decided value.

This taking into account of a weighting function of the difference between the equalized signal and the value decided in the error signal makes it possible to improve the control of the increase of the noise, while simultaneously carrying out a control of the asymmetry of the noise.

The invention also makes it possible to favor the equalization of one level rather than the other.

Advantageously, the function of the equalized signal, respectively of the decided value, comprises a difference between a reference level and the equalized signal, respectively the decided value.

The reference level can be chosen according to a distribution of noise affecting the transmission channel.

Advantageously, when a binary error rate is available at the output of the transmission channel, a ratio between one part and the other is determined. additive and a multiplicative part of the noise affecting the transmission channel from the bit error rate and the reference level. This makes it possible to characterize the nature of the noise affecting the transmission channel and thus to identify the main source that generates it. The invention is advantageously used when the transmission channel is an optical channel, or more generally a channel such that the noise that affects this channel depends on the signal. This is the case for example when the noise comprises an additive part and a multiplicative part.

. The invention further provides a receiver arranged to decide the value of a received signal. The receiver in question comprises means for implementing the method mentioned above.

The invention also proposes a computer program product comprising instructions adapted to the implementation of the method mentioned above, when said program is loaded and executed by computer means of a receiver.

Other features and advantages of the present invention will become apparent in the following description of nonlimiting exemplary embodiments, with reference to the appended drawings, in which:

FIG. 1 is a diagram showing a functional architecture of a receiver capable of implementing the invention;

FIG. 2a is an example of a white Gaussian additive noise distribution;

FIG. 2b is an example of a noise distribution affecting an optical transmission channel;

FIGS. 3a, 3b and 3c each show an example of calculating an error signal according to the invention.

FIG. 1 shows a signal x (t) received at a receiver 5. This signal x (t) is for example received from an optical transmission channel. The signal x (t) is then equalized in a manner known per se with the aid of an equalizer 6. For this purpose, the signal x (t) undergoes an integer n of successive delays T, so that we have n + 1 copies of the signal x (t) shifted in time. These different copies are then weighted by coefficients Co, c- _t , ..., C _n respectively, then summed in a summation module 2. The operation of equalization takes advantage of the information redundancy existing between the different copies of the signal x (t) shifted in time, so that there is then an equalized signal y (t) whose inter-symbol interference ISI is reduced. Subsequently, the equalized signal y (t) is introduced into a decision module 4, which consists, for example, of a decision gate comparing the value of the signal y (t) with a decision threshold Uth. This operation results in a decision signal d (t). Since the signals considered are generally digital, the decision signal d (t) advantageously consists of a sequence of bits.

It should be noted that the signals mentioned above are generally sampled so that the samples are considered separately thereafter. We then note y a given sample obtained from the equalized signal y (t) and a corresponding sample of the decision signal A module 3 calculates an error signal e. This error signal aims at estimating the differences between the equalized signal y and the signal actually transmitted and which would have been received as such at the receiver 5 in the absence of noise and distortions on the transmission channel. As the transmitted signal is generally unknown to the receiver 5, the error signal is determined from the equalized signal y on the one hand and the decision signal d on the other hand. Such an approximation is considered reliable as long as the bit error rate is low. The error signal e is also used to update the coefficients Co, ci, ..., C _n of the equalizer 6.

Note that the LMS algorithm uses this mode of operation. In the case of LMS, the error signal is calculated as a difference between the equalized signal and the decision signal, ie y-d.

According to the present invention, the module 3 implements a different calculation of the LMS algorithm which makes it possible to preserve a possible asymmetry in the noise affecting the transmission channel from which the signal x (t) is received. This calculation weights the difference between the equalized signal and the decision signal by a function of the equalized signal y and / or a function of the decision signal d. FIGS. 3a, 3b and 3c give three examples of calculation implemented by the module 3 of FIG. 1 in the context of the present invention. In the example of Figure 3a, the difference yd is weighted by a function fi of y. For example, the function f | can understand the difference between a Refi reference threshold and y. In this case, we get e = (Refry). (Yd).

Such a calculation mode is particularly advantageous when the noise affecting the transmission channel from which x (t) is received is asymmetrical and depends on the signal itself. A distribution of such noise is illustrated in Figure 2b. In this example, the transmission channel is an optical channel affected by a noise that can be decomposed into an additive part and a multiplicative part, after detection. The transmitted signal is binary so that it only takes the values '0' or '1'. The received signal values are therefore between 0 and 1 (we have in fact an eye diagram with 4 states 0, α, 1-α and 1, where α represents the ISI level for the channel considered). It can be seen in this example that the noise is particularly strong around the binary value 1 and the value 1-α. The noise is lower around the values 0 and α.

Variances σ-i ² σ i _^-α-2 _σ α ^2, σo ² noise signal for each state have been indicated in Figure 2b, where T ₀ represents the noise contribution of additive nature and Ti represents the contribution to noise of a multiplicative nature. It thus clearly emerges from this example that the total noise is asymmetrical, that is to say that it affects the binary values '1' more than the binary values '0' transmitted on the optical channel. By comparison, FIG. 2a illustrates a noise distribution in the case of an additive noise transmission channel. This shows a perfect symmetry of the noise (which is AWGN in this case), which results in an equality of the noise variances for the four states at the value IV, where r _th represents a thermal noise.

It is thus understood that, in the case illustrated in FIG. 2b, which represents the distribution before equalization, a decision consisting of a comparison between an intermediate threshold and the detected signal value would favor the bad decisions. On the other hand, if the decision threshold is chosen to be closer to the value 0 than the value 1, the chances of good decisions are increased when a '0' is transmitted. This is due to fact that the ¹ O ¹ (unlike '1') are little impacted by noise. It is therefore in our interest to maintain the asymmetry of noise to improve decision-making.

The error signal calculation performed by the module 6 of the receiver 5 and illustrated in FIG. 3a makes it possible to better preserve the asymmetry of the noise. Indeed, calculating the error signal such as e = (Refry). (Y-d) makes it possible to attenuate the importance of the decision errors related to the high level of noise impacting

'1'. The updating of the equalizer weighting coefficients on this basis thus makes it possible to preserve the asymmetry of the noise, in particular by limiting the noise added during the equalization of the ¹ O '. This therefore leads to better performance than in the case where the LMS algorithm is used.

The reference threshold Refi is advantageously chosen as a function of the maximum power in reception and the ratio between the multiplicative noise and the additive noise on the transmission channel considered. It may also depend on channel characteristics that determine the amount of continuous noise versus signal-dependent noise. Advantageously, the value of the threshold is acquired by learning during the establishment of the channel. The threshold value can be further modified over time.

When a bit error rate (BER) estimate is available at the receiver 5, BER and Refi values can further be deduced from a ratio between the additive and the multiplicative noise. This makes it possible to know which source of noise is dominant on the channel considered.

FIG. 3b shows a second example of calculating the error signal implemented by the module 3 of FIG. 1. In this example, the difference yd is weighted by a function f _{2 that} depends on the decision signal d and possibly on a reference threshold Ref ₂ . In mathematical form, one can for example write: e ⁼ f ₂ (d, Ref ₂ ). (Yd).

In an exemplary embodiment where f ₂ (d, Ref ₂ ) = Ref ₂ -d and where the signals considered are normalized, so that the maximum power in reception is equal to 1, we can then choose Ref ₂ equal to 1. This then amounts to ignoring the equalization of the '1' and reducing I ¹ ISI, while controlling the noise level, only for the '0' transmitted (since in this case we have: e = (1-d). (yd), ie e = 0 if d = 1 and e = y if d = 0). This is however a theoretical example. Preferably, a value of Ref ₂ close to 1, 5 can be used in this case, to take into account the two types of noise, additive and multiplicative.

A third example is given in Figure 3c. In this case, a function f ₃ and a function U are respectively applied to the signals y and d, before weighting the difference yd. Reference thresholds Ref ₃ and Ref ₄ respectively can also be used, so that e = f ₃ (y _> Ref ₃ ) .f ₄ (d, Ref ₄ ). (Yd).

The preceding remarks concerning Refi can of course apply to the reference thresholds Ref ₂ , Ref ₃ and Ref ₄ .

Note that the invention can be implemented by a receiver such as the receiver 5 of Figure 1. It can also be implemented using a computer program including instructions adapted for this purpose . In the latter case, the program is then loaded and executed by computer means for example the receiver 5 itself.

Claims

CLAIM CATIONS

A method for deciding the value of a received signal, comprising the steps of:

- receive a signal (x (t)) from a transmission channel; equalizing the received signal by summing several copies of the signal shifted in time and weighted by respective coefficients (co, ci, ..., C _n );

- decide the value of the received signal from the equalized signal;

- determining an error signal (e) dependent on a difference between the equalized signal (y) and the decided value (d); and

updating said coefficients as a function of the determined error signal; characterized in that the error signal comprises a weighting of the difference between the equalized signal and the value decided by at least one of a function (fi, fβ) of the equalized signal and a function (f ₂ , U) of the value decided.

2. Method according to claim 1, wherein the function (fi, f ₃ , f ₂ , f ₄ ) of the equalized signal (y), respectively of the decided value (d), comprises a difference between a reference level (Ref. -i, Refβ, Ref2, Ref ₄ ) and the equalized signal, respectively the decided value.

The method of claim 2, wherein the reference level

(Ref-i, Ref2, Ref ₃ , Ref ₄ ) depends on the noise affecting the transmission channel.

4. The method according to claim 3, wherein a bit error rate is available for the transmission channel and a ratio between an additive part and a multiplicative part of the noise affecting the transmission channel is determined from the transmission rate. binary error and reference level (Refi, Ref ₂ , Ref ₃ , Ref ₄ ).

The method of any one of the preceding claims, wherein the transmission channel is an optical channel.

Receiver (5) arranged to decide the value of a received signal (x (t)), the receiver comprising means for implementing the method according to any one of the preceding claims.

7. Computer program product comprising instructions adapted to implement the method according to any one of claims 1 to 5, when said program is loaded and executed by computer means of a receiver (5).